Our version of the Carrollian Liouville action throws up very interesting avenues of further research. The difference with the limiting analysis of [1]} is intriguing. It would mean that there is potentially another limit that yields the Carrollian Liouville action. (We try and distinguish it from the earlier work in the literature by calling this Carrollian Liouville as opposed to BMS Liouville.) It would be instructive to construct this limit explicitly in the relativistic Liouville theory and understand what it means. It would also be very interesting to figure out how one can modify the analysis of [2]} to get the Carrollian Liouville theory starting out from a Chern-Simons formulation of 3d asymptotically flat gravity, then going over to a WZW model and then doing a Hamiltonian reduction.
